Problem: Solve for $x$ and $y$ using substitution. ${-4x+3y = -12}$ ${y = 2x-10}$
Explanation: Since $y$ has already been solved for, substitute $2x-10$ for $y$ in the first equation. ${-4x + 3}{(2x-10)}{= -12}$ Simplify and solve for $x$ $-4x+6x - 30 = -12$ $2x-30 = -12$ $2x-30{+30} = -12{+30}$ $2x = 18$ $\dfrac{2x}{{2}} = \dfrac{18}{{2}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {y = 2x-10}\thinspace$ to find $y$ ${y = 2}{(9)}{ - 10}$ $y = 18 - 10$ $y = 8$ You can also plug ${x = 9}$ into $\thinspace {-4x+3y = -12}\thinspace$ and get the same answer for $y$ : ${-4}{(9)}{ + 3y = -12}$ ${y = 8}$